Matrix Query Languages

2021 ◽  
Vol 50 (3) ◽  
pp. 6-19
Author(s):  
Floris Geerts ◽  
Thomas Muñoz ◽  
Cristian Riveros ◽  
Jan Van den Bussche ◽  
Domagoj Vrgoč
Keyword(s):  
Linear Algebra ◽  
Data Analytics ◽  
Query Language ◽  
Query Languages ◽  
Arithmetic Circuits ◽  
Matrix Operations ◽  
The Matrix

Due to the importance of linear algebra and matrix operations in data analytics, there has been a renewed interest in developing query languages that combine both standard relational operations and linear algebra operations. We survey aspects of the matrix query language MATLANG and extensions thereof, and connect matrix query languages to classical query languages and arithmetic circuits.

scholarly journals A note on the eigenvalue free intervals of some classes of signed threshold graphs

2019 ◽  
Vol 7 (1) ◽  
pp. 218-225
Author(s):  
Milica Anđelić ◽  
Tamara Koledin ◽  
Zoran Stanić
Keyword(s):  
Tridiagonal Matrix ◽  
Constant Sign ◽  
Equitable Partition ◽  
Elementary Matrix ◽  
Matrix Operations ◽  
Threshold Graphs ◽  
The Matrix ◽  
Threshold Graph

Abstract We consider a particular class of signed threshold graphs and their eigenvalues. If Ġ is such a threshold graph and Q(Ġ ) is a quotient matrix that arises from the equitable partition of Ġ , then we use a sequence of elementary matrix operations to prove that the matrix Q(Ġ ) – xI (x ∈ ℝ) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which Ġ has no eigenvalues.

MRHS solver based on linear algebra and exhaustive search

2018 ◽  
Vol 12 (3) ◽  
pp. 143-157 ◽  
Author(s):  
Håvard Raddum ◽  
Pavol Zajac
Keyword(s):  
Linear Algebra ◽  
Matrix Representation ◽  
Equation System ◽  
Exhaustive Search ◽  
Binary Matrix ◽  
Algebraic Attacks ◽  
The Matrix ◽  
Speed Up ◽  
Symmetric Key

Abstract We show how to build a binary matrix from the MRHS representation of a symmetric-key cipher. The matrix contains the cipher represented as an equation system and can be used to assess a cipher’s resistance against algebraic attacks. We give an algorithm for solving the system and compute its complexity. The complexity is normally close to exhaustive search on the variables representing the user-selected key. Finally, we show that for some variants of LowMC, the joined MRHS matrix representation can be used to speed up regular encryption in addition to exhaustive key search.

DMRG Approach to Fast Linear Algebra in the TT-Format

2011 ◽  
Vol 11 (3) ◽  
pp. 382-393 ◽  
Author(s):  
Ivan Oseledets
Keyword(s):  
Linear Systems ◽  
Linear Algebra ◽  
Direct Method ◽  
Fast Algorithms ◽  
Approximate Solutions ◽  
Vector Product ◽  
The Matrix ◽  
Minimization Scheme

AbstractIn this paper, the concept of the DMRG minimization scheme is extended to several important operations in the TT-format, like the matrix-by-vector product and the conversion from the canonical format to the TT-format. Fast algorithms are implemented and a stabilization scheme based on randomization is proposed. The comparison with the direct method is performed on a sequence of matrices and vectors coming as approximate solutions of linear systems in the TT-format. A generated example is provided to show that randomization is really needed in some cases. The matrices and vectors used are available from the author or at http://spring.inm.ras.ru/osel

Application of Fuzzy Petri Nets in Hydraulic Pump Fault Diagnosis

2014 ◽  
Vol 1008-1009 ◽  
pp. 1176-1179
Author(s):  
Hai Dong ◽  
Heng Bao Xin
Keyword(s):  
Fault Diagnosis ◽  
Petri Nets ◽  
Hydraulic Pump ◽  
Modeling And Analysis ◽  
Matrix Operations ◽  
Knowledge Reasoning ◽  
Fuzzy Production Rules ◽  
The Matrix ◽  
Fuzzy Petri Nets ◽  
Definition Of

In this paper, an approach of fuzzy Petri nets (FPN) is proposed to simulate the fault spreading and diagnosis of hydraulic pump. First, the fuzzy production rules and the definition of FPN were briefly introduced. Then, its knowledge reasoning process and the matrix operations based on an algorithm were conducted, which makes full use of its parallel reasoning ability and makes it simpler and easier to implement. Finally, a case of hydraulic pump fault diagnosis with FPN was presented in detail, for illustrating the interest of the proposed modeling and analysis algorithm.

DocBase

2013 ◽  
pp. 365-393
Author(s):  
Arijit Sengupta ◽  
Ramesh Venkataraman
Keyword(s):  
Query Processing ◽  
Query Language ◽  
Formal Model ◽  
Query Languages ◽  
Prototype System ◽  
Storage And Retrieval ◽  
Visual Query Formulation ◽  
Visual Query ◽  
Nested Relations ◽  
Entity Relationship

This chapter introduces a complete storage and retrieval architecture for a database environment for XML documents. DocBase, a prototype system based on this architecture, uses a flexible storage and indexing technique to allow highly expressive queries without the necessity of mapping documents to other database formats. DocBase is an integration of several techniques that include (i) a formal model called Heterogeneous Nested Relations (HNR), (ii) a conceptual model XER (Extensible Entity Relationship), (ii) formal query languages (Document Algebra and Calculus), (iii) a practical query language (Document SQL or DSQL), (iv) a visual query formulation method with QBT (Query By Templates), and (v) the DocBase query processing architecture. This paper focuses on the overall architecture of DocBase including implementation details, describes the details of the query-processing framework, and presents results from various performance tests. The paper summarizes experimental and usability analyses to demonstrate its feasibility as a general architecture for native as well as embedded document manipulation methods.

Applications

2004 ◽  
Author(s):  
Wesley Petersen ◽  
Peter Arbenz
Keyword(s):  
Linear Algebra ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Simple Procedure ◽  
Complex Numbers ◽  
Multiprocessor Computer ◽  
Basic Linear Algebra Subprograms ◽  
The Matrix ◽  
Shared Memory Multiprocessor ◽  
Real Complex

Linear algebra is often the kernel of most numerical computations. It deals with vectors and matrices and simple operations like addition and multiplication on these objects. Vectors are one-dimensional arrays of say n real or complex numbers x0, x1, . . . , xn−1. We denote such a vector by x and think of it as a column vector, On a sequential computer, these numbers occupy n consecutive memory locations. This is also true, at least conceptually, on a shared memory multiprocessor computer. On distributed memory multicomputers, the primary issue is how to distribute vectors on the memory of the processors involved in the computation. Matrices are two-dimensional arrays of the form The n · m real (complex) matrix elements aij are stored in n · m (respectively 2 · n ·m if complex datatype is available) consecutive memory locations. This is achieved by either stacking the columns on top of each other or by appending row after row. The former is called column-major, the latter row-major order. The actual procedure depends on the programming language. In Fortran, matrices are stored in column-major order, in C in row-major order. There is no principal difference, but for writing efficient programs one has to respect how matrices are laid out. To be consistent with the libraries that we will use that are mostly written in Fortran, we will explicitly program in column-major order. Thus, the matrix element aij of the m×n matrix A is located i+j · m memory locations after a00. Therefore, in our C codes we will write a[i+j*m]. Notice that there is no such simple procedure for determining the memory location of an element of a sparse matrix. In Section 2.3, we outline data descriptors to handle sparse matrices. In this and later chapters we deal with one of the simplest operations one wants to do with vectors and matrices: the so-called saxpy operation (2.3). In Tables 2.1 and 2.2 are listed some of the acronyms and conventions for the basic linear algebra subprograms discussed in this book.

Querying GML

2010 ◽  
pp. 11-19 ◽  
Author(s):  
Jose E. Córcoles ◽  
Pascual González
Keyword(s):  
Spatial Data ◽  
Query Language ◽  
Query Languages ◽  
Structured Data ◽  
Large Set ◽  
Topological Relationship ◽  
Xml Document ◽  
Spatial Operators

As a database format, XML (GML by extension) can be queried. In order to do this, we need a query language (of general use) to retrieve information from an XML document. Nevertheless, it is necessary to enrich the query language over XML features with spatial operators if we wish to apply it over spatial data encoded with GML. Otherwise, these query languages could only be used to query alphanumeric features of an XML document and not, for example, the topological relationship between two spatial regions. Today, there is a large set of query languages over XML. These query languages are different with respect to syntax, available operators and environment of applicability. However, they share the same features, that is, features of query languages over semi-structured data. With respect to GML, from the literature, it is known that four GML query languages have been proposed. The following chapter briefly describes these query languages over GML.

scholarly journals Generating a Cancellable Fingerprint using Matrices Operations and Its Fingerprint Processing Requirements

2018 ◽  
Vol 14 (6) ◽  
pp. 1 ◽  
Author(s):  
Riki Mukhaiyar
Keyword(s):  
Region Of Interest ◽  
Original Form ◽  
Biometric Data ◽  
Matrix Operations ◽  
The Matrix ◽  
Robust Image ◽  
Reciprocal Matrix ◽  
Processing Steps ◽  
Fingerprint Feature

Cancellable fingerprint uses transformed or intentionally distorted biometric data instead of the original biometric data for identifying person. When a set of biometric data is found to be compromised, they can be discarded, and a new set of biometric data can be regenerated. This initial principal is identical with a non-invertible concept in matrices operations. In matrix domain, a matrix cannot be transformed into its original form if it meets several requirements such as non-square form matrix, consist of one zero row/column, and no row as multiple of another row. These conditions can be acquired by implementing three matrix operations using Kronecker Product (KP) operation, Elementary Row Operation (ERO), and Inverse Matrix (INV) operation. KP is useful to produce a non-square form matrix, to enlarge the size of matrix, to distinguish and disguise the element of matrix by multiplying each of elements of the matrix with a particular matrix. ERO can be defined as multiplication and addition force to matrix rows. INV is utilized to transform one matrix to another one with a different element or form as a reciprocal matrix of the original. These three matrix operations should be implemented together in generating the cancellable feature to robust image. So, if once three conditions are met by imposter, it is impossible to find the original image of the fingerprint. The initial aim of these operations is to camouflage the original look of the fingerprint feature into an abstract-look to deceive an un-authorized personal using the fingerprint irresponsibly. In this research, several fingerprint processing steps such as fingerprint pre-processing, core-point identification, region of interest, minutiae extration, etc; are determined to improve the quality of the cancellable feature. Three different databases i.e. FVC2002, FVC2004, and BRC are utilized in this work.

Performance Analysis of the PISO-Based CFD Simulation

2014 ◽  
Vol 607 ◽  
pp. 872-876 ◽  
Author(s):  
Xiao Guang Ren
Keyword(s):  
Performance Optimization ◽  
Execution Time ◽  
Cfd Simulation ◽  
Fluid Flows ◽  
Total Execution Time ◽  
Simulation Performance ◽  
Simulation Efficiency ◽  
Matrix Operations ◽  
The Matrix ◽  
Computational Fluid Dynamics Cfd

Computational Fluid Dynamics (CFD) is widely applied for the simulation of fluid flows, and the performance of the simulation process is critical for the simulation efficiency. In this paper, we analyze the performance of CFD simulation application with profiling technology, which gets the portions of the main parts’ execution time. Through the experiment, we find that the PISO algorithm has a significant impact on the CFD simulation performance, which account for more than 90% of the total execution time. The matrix operations are also account for more than 60% of the total execution time, which provides opportunity for performance optimization.

A Trust Evaluation of Networks Utilizing Matrix Operations Based on t-norms and t-conorms

2012 ◽  
Vol 16 (1) ◽  
pp. 154-161
Author(s):  
Masaya Nohmi ◽  
◽  
Aoi Honda ◽  
Yoshiaki Okazaki
Keyword(s):  
Trust Evaluation ◽  
Matrix Operations ◽  
Fuzzy Graphs ◽  
Algebraic Properties ◽  
The Matrix ◽  
Membership Value

A new scheme for numerical trust evaluation of networks is proposed. Matrix operations based on t-norms and t-conorms are used for the evaluation. The algebraic properties of the matrix operations are studied. Fuzzy graphs, in which nodes are linked with some membership value, are proposed, using the matrices as adjacent matrices. Furthermore, the fuzzinesses of the trustability distribution are calculated.

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